Microscopic derivation of Dirac composite fermion theory: Aspects of noncommutativity and pairing instabilities,Physical Review B

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Microscopic derivation of Dirac composite fermion theory: Aspects of noncommutativity and pairing instabilities
Physical Review B ( IF 3.2 ) Pub Date : 2021-09-23 , DOI: 10.1103/physrevb.104.115150
Dragoljub Gočanin ₁ , Sonja Predin ₂ , Marija Dimitrijević Ćirić ₁ , Voja Radovanović ₁ , Milica Milovanović ₃

Affiliation

Building on previous work [N. Read, Phys. Rev. B 58, 16262 (1998); Z. Dong and T. Senthil, Phys. Rev. B 102, 205126 (2020)] on the system of bosons at filling factor

ν = 1

, we derive the Dirac composite fermion theory for a half-filled Landau level from first principles and apply the Hartree-Fock approach in a preferred representation. On the basis of the microscopic formulation, in the long-wavelength limit, we propose a noncommutative field-theoretical description, which in a commutative limit reproduces the Son's theory, with additional terms that may be expected on physical grounds. The microscopic representation of the problem is also used to discuss pairing instabilities of composite fermions. We find that a presence of a particle-hole symmetry breaking leads to a weak (BCS) coupling

p

-wave pairing in the lowest Landau level, and strong coupling

p

-wave pairing in the second Landau level that occurs in a band with nearly flat dispersion, a third power function of momentum.

中文翻译：

狄拉克复合费米子理论的微观推导：非对易性和配对不稳定性的方面

建立在以前的工作 [N. 阅读，物理。修订版 B 58 , 16262 (1998)；Z. Dong 和 T. Senthil，物理。Rev. B 102 , 205126 (2020)] 关于填充因子的玻色子系统

ν = 1

，我们从第一性原理推导出半填充朗道能级的狄拉克复合费米子理论，并在首选表示中应用 Hartree-Fock 方法。在微观公式的基础上，在长波长极限中，我们提出了一种非交换场论描述，它在交换极限中再现了 Son 的理论，并带有可能在物理基础上预期的附加项。该问题的微观表示也用于讨论复合费米子的配对不稳定性。我们发现粒子-空穴对称性破坏的存在导致弱（BCS）耦合